Bushfires pose significant environmental and societal challenges, and understanding how they propagate is important for improving prediction and mitigation strategies. We study a model for wildfire propagation, analyzing a nonlocal parabolic partial differential equation posed in thin tubular domains modeling narrow gullies.

 

In this talk, we discuss the effective behaviour of the system as the width of the gully becomes very small. In this asymptotic regime, the model undergoes a dimensional reduction, turning the original problem into a geometric evolution equation posed on the axis of the gully.